7.2 problem Ex 2

Internal problem ID [10135]

Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section: Chapter 2, differential equations of the first order and the first degree. Article 14. Equations reducible to linear equations (Bernoulli). Page 21
Problem number: Ex 2.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_separable]

Solve \begin {gather*} \boxed {y^{\prime } y+y^{2} x -x=0} \end {gather*}

Solution by Maple

Time used: 0.0 (sec). Leaf size: 33

dsolve(y(x)*diff(y(x),x)+x*y(x)^2=x,y(x), singsol=all)
 

\begin{align*} y \relax (x ) = \sqrt {{\mathrm e}^{-x^{2}} c_{1}+1} \\ y \relax (x ) = -\sqrt {{\mathrm e}^{-x^{2}} c_{1}+1} \\ \end{align*}

Solution by Mathematica

Time used: 1.927 (sec). Leaf size: 57

DSolve[y[x]*y'[x]+x*y[x]^2==x,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\sqrt {1+e^{-x^2+2 c_1}} \\ y(x)\to \sqrt {1+e^{-x^2+2 c_1}} \\ y(x)\to -1 \\ y(x)\to 1 \\ \end{align*}